Is it possible that a theory that can describe the universe at the planck scale can violate things that we now consider fundamental in nature?For example can it violate rotational and translational invariance and subsequently momentum wouldn't be conserved ?Should one consider these invariance principles to be fundamental that we must choose the lagrangian to respect them ?

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Conservation laws in theory are valid because they rest on solid and innumerable data. An experiment finding non-conservation of a law supported by theory would immediately invalidate the theory.

Our experimental experience is that the two laws you mention, conservation of angular momentum and momentum are such universal laws within the data we can access.

Theories are a different matter. Theories can be extended to variable and parameter regions where experiments cannot go at present or possibly ever. This does not necessarily mean that the extension of these theories will hold willy nilly in the unexplorable experimentally regions,( i.e. the conservation laws should also hold there experimentally). It is only necessary that at the limit where we know from the data that the conservation laws hold, the theories for the extended region reproduce the behavior of the standard theories, i.e. conserve these laws .

In once sense, the quantities you mention get violated all the time in quantum mechanics. Furthermore, it happens at levels that are far less ferocious, inaccessible, and hypothetical (if you can't get there it's hypothetical, by definition) than the Planck scale. Such violations rely on quantum uncertainty and result in various forms and combinations of virtual particles, that is, particles that "sort of" exist if you look at the world using sufficiently short time scales. Virtual particles have real, measurable impacts on everyday physics, e.g. screening or "blurring" of nuclear charge in atoms, which impacts chemistry. But on the average, such violations cannot endure in the face of the absolute conservation laws of physics.

Yeah, they should do to start with, unless their abandonment simplifies the theory while still predicting experimental observation. Bohr was prepared to abandon the conservation of energy principle at the quantum level to account for the apparent loss of energy in some interactions. Pauli on the other hand came up with the idea of a weakly interacting particle, the neutrino, carrying away excess energy - and he was right in the end.